Leak on gas heater water line?

I discovered a serious leak on the flexible copper cold water supply line to our main water heater. The leak seems to be coming out from just behind the fitting that screws onto the straight copper pipe.

I shut down most of the leak by tightening the fitting, but there is still a very tiny seepage, you can only feel it.

What could cause this leak? And will simply replacing the flexible line take care of the problem?

An odd note, the shutoff valve is located on the HOT water line. Which means I'm trying to figure out how to replace the leaking line without filling the entire supply system with air.